In a long-term comparative clinical trial in chronic diseases it is desirable from an ethical standpoint as well as an economic one to periodically examine accumulatng data to see if early stopping of the trial is indicated. It will frequently be desirable that the statistical inferences of interest pertain to the completion of data collection as originally conceived when the trial was initiated. Clinical trial designs and corresponding statistical analyses have been suggested which permit specification of systematic algorithms to do periodic extreme case analyses which may suggest early stopping because the results of statistical analyses using all data collected or to be collected is already known with certainty. This requirement of certainty as to the final outcome of statistical analysis seems somewhat extreme. It would appear adequate for the decision-making process at any point in time to merely have a high probability that acquisition of further data will lead to rejection (acceptance) of the null hypothesis. For the clinical trial designs which have been suggested and a variety of non-parametric statistical analyses, it is proposed to explore the asymptotic behavior of probabilistic stopping, particularly with respect to the probability distribution of the observed fraction of expected number of events till appropriateness of early stopping is indicated. Classical, mathematical and statistical methods applicable to asymptotic distribution theory will be the main analysis tools. Computer simulation will be an essential tool to get some indication of how large trials must be for the asymptotic theory to be applicable. The impact of such practical matters as the typical somewhat protracted period of entry of patients into a trial will be assessed.